Skip to content

IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Estimation procedures for lifetime distributions

Lives enter a study at various ages and are observed until death or censoring. For a life entering at age 50 who is censored at age 58 (no death), under a model with survival function S, which is the correct likelihood contribution?

The contribution is S(58)/S(50). Entry at age 50 is left truncation, so we condition on survival to 50, and censoring at 58 tells us only that the life survived beyond 58, giving the conditional survival probability.

  1. AS(58)
  2. BS(58)/S(50)Correct
  3. CS(50)/S(58)
  4. Df(58)/S(50)
  5. 1 − S(58)/S(50)

Explanation

Entry at 50 means left truncation, so we condition on survival to 50. Censoring at 58 means survival beyond 58 is all that is known. The contribution is P(T>58 | T>50) = S(58)/S(50). Option 1 omits the conditioning, and option 4 is the death-contribution form. Option 5 is the probability of death before 58.

Did you get it right without looking?

One question tells you little. A timed set on Estimation procedures for lifetime distributions shows your real accuracy, how long you take and where you lose marks.

Practise Estimation procedures for lifetime distributionsFree diagnostic mock

More Estimation procedures for lifetime distributions questions